dbdt01.f3

Usage

Functions/Subroutines

subroutine dbdt01 (m, n, kd, a, lda, q, ldq, d, e, pt, ldpt, work, resid)
DBDT01

Function/Subroutine Documentation

subroutine dbdt01 (integer m, integer n, integer kd, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldpt, * ) pt, integer ldpt, double precision, dimension( * ) work, double precision resid)

DBDT01

Purpose:

!>
!> DBDT01 reconstructs a general matrix A from its bidiagonal form
!>    A = Q * B * P**T
!> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
!> matrices and B is bidiagonal.
!>
!> The test ratio to test the reduction is
!>    RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
!> where EPS is the machine precision.
!>

Parameters

!>          M is INTEGER
!>          The number of rows of the matrices A and Q.
!>

!>          N is INTEGER
!>          The number of columns of the matrices A and P**T.
!>

!>          KD is INTEGER
!>          If KD = 0, B is diagonal and the array E is not referenced.
!>          If KD = 1, the reduction was performed by xGEBRD; B is upper
!>          bidiagonal if M >= N, and lower bidiagonal if M < N.
!>          If KD = -1, the reduction was performed by xGBBRD; B is
!>          always upper bidiagonal.
!>

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The m by n matrix A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          The m by min(m,n) orthogonal matrix Q in the reduction
!>          A = Q * B * P**T.
!>

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  LDQ >= max(1,M).
!>

!>          D is DOUBLE PRECISION array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B.
!>

!>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
!>          The superdiagonal elements of the bidiagonal matrix B if
!>          m >= n, or the subdiagonal elements of B if m < n.
!>

!>          PT is DOUBLE PRECISION array, dimension (LDPT,N)
!>          The min(m,n) by n orthogonal matrix P**T in the reduction
!>          A = Q * B * P**T.
!>

LDPT

!>          LDPT is INTEGER
!>          The leading dimension of the array PT.
!>          LDPT >= max(1,min(M,N)).
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (M+N)
!>

RESID

!>          RESID is DOUBLE PRECISION
!>          The test ratio:
!>          norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 139 of file dbdt01.f.